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Students' Depictions of Quantum Mechanics Students’ depictions of quantum mechanics: a contemporary review and some implications for research and teaching Johan Falk January 2007 Dissertation for the degree of Licentiate of Philosophy in Physics within the specialization Physics Education Research Uppsala University, 2007 Abstract This thesis presents a comprehensive review of research into students’ depic- tions of quantum mechanics. A taxonomy to describe and compare quantum mechanics education research is presented, and this taxonomy is used to highlight the foci of prior research. A brief history of quantum mechanics education research is also presented. Research implications of the review are discussed, and several areas for future research are proposed. In particular, this thesis highlights the need for investigations into what interpretations of quantum mechanics are employed in teaching, and that classical physics – in particular the classical particle model – appears to be a common theme in students’ inappropriate depictions of quantum mechanics. Two future research projects are presented in detail: one concerning inter- pretations of quantum mechanics, the other concerning students’ depictions of the quantum mechanical wave function. This thesis also discusses teaching implications of the review. This is done both through a discussion on how Paper 1 can be used as a resource for lecturers and through a number of teaching suggestions based on a merging of the contents of the review and personal teaching experience. List of papers and conference presentations Falk, J & Linder, C. (2005). Towards a concept inventory in quantum mechanics. Presentation at the Physics Education Research Conference, Salt Lake City, Utah, August 2005. Falk, J., Linder, C., & Lippmann Kung, R. (in review, 2007). Review of empirical research into students’ depictions of quantum mechanics. Manuscript submitted to Educational Research Review. Table of contents 1 Introduction.................................................................................................. 1 1.1 Introduction to the problem................................................................. 1 1.1.1 The importance of quantum mechanics...................................... 1 1.1.2 The importance of quantum mechanics education research ..... 3 1.2 Significance of this thesis.................................................................... 4 1.3 Introduction to physics education research ........................................ 6 1.3.1 Conceptual understanding and “misconceptions” ..................... 6 1.3.2 Research into physics teaching ................................................... 8 1.3.3 Models for describing physics learning...................................... 9 1.3.4 Physics education research in relation to quantum mechanics educations research................................................................................. 10 1.4 Introduction to quantum mechanics.................................................. 11 1.4.1 The context of quantum mechanics .......................................... 11 1.4.2 States, eigenstates and probabilities ......................................... 12 1.4.3 Spatial distribution..................................................................... 12 1.4.4 The Schrödinger equation ......................................................... 13 1.4.5 Some comments......................................................................... 14 2 Introduction to Paper 1 .............................................................................. 15 2.1 The purpose of Paper 1...................................................................... 15 2.1.1 Student depictions?.................................................................... 15 3 Review method .......................................................................................... 17 3.1 Why a review method?...................................................................... 17 3.2 Phase A: starting point....................................................................... 17 3.3 Phase B: pre-study ............................................................................. 18 3.4 Phase C: main literature study .......................................................... 18 3.5 Phase D: finalising the review .......................................................... 19 4 Significance of Paper 1.............................................................................. 20 4.1 What does this literature review mean for researchers?.................. 20 4.1.1 Introduction to research and resource list................................. 20 4.1.2 Taxonomy................................................................................... 21 4.1.3 Suggesting research questions .................................................. 21 4.1.4 Historical overview.................................................................... 21 4.2 What does this literature review mean for lecturers? ...................... 22 4.2.1 Introduction to education research............................................ 22 4.2.2 Awareness that students have problems in quantum mechanics 22 4.2.3 Awareness of inappropriate depictions .................................... 23 4.3 Suggestions for teaching ................................................................... 23 4.3.1 Recognise the influence of the examinations........................... 24 4.3.2 Make use of “easy” questions ................................................... 24 4.3.3 Emphasise difference with classical mechanics ...................... 25 4.3.4 Mention interpretations of quantum mechanics....................... 26 4.3.5 Concerning atoms and orbitals.................................................. 26 4.3.6 Concerning the wave-nature of matter ..................................... 26 4.3.7 Concerning one-dimensional square potentials ....................... 27 4.3.8 Concerning time-dependence.................................................... 28 4.3.9 Concerning Dirac notation ........................................................ 28 4.3.10 Use quantum mechanics as a theme in physics education .... 29 5 Description of research plans.................................................................... 31 5.1 Study 1: What standard interpretation? ............................................ 31 5.1.1 Research questions..................................................................... 32 5.1.2 Research method........................................................................ 33 5.1.3 Reporting.................................................................................... 33 5.1.4 Possible ways of expanding the project ................................... 33 5.2 Study 2: Students’ depictions of the quantum wave function......... 34 5.2.1 Research questions..................................................................... 35 5.2.2 Research method........................................................................ 35 5.2.3 Theoretical framework for analysis.......................................... 36 5.2.4 Possible ways of expanding the project ................................... 36 6 Sammanfattning på svenska...................................................................... 38 7 Acknowledgements ................................................................................... 40 8 References .................................................................................................. 41 Paper 1 Appendix 1 Appendix 2 1. Introduction 1.1. Introduction to the problem Possibly the greatest joy of conducting education research in quantum me- chanics is the feeling of making a substantial contribution to a research field that is very important. Although I am aware that each researcher probably considers her or his own research field as particularly important, I cannot help feeling that I am particularly favoured in my choice of research field, since the necessity of quantum mechanics education research is dramatically obvious. Why is this? In short, it is because quantum mechanics is an extremely important and influential physics theory, and because teaching and learning quantum mechanics is a challenging task for both lecturers and students. In this section I will elaborate on this, in order to make the importance of quan- tum mechanics education research clear. 1.1.1. The importance of quantum mechanics I believe that most physicists if asked by a non-physicist whether quantum mechanics is important, would start to smile. Some would do this out of sheer politeness. A few would possibly do it while thinking “how can any- one ask such a stupid question?” But most, I believe, would do it because they feel that they finally have a physics question that they can answer in a way that laypeople would understand. To a physicist, the importance of quantum mechanics is self evident. She, or he, knows that quantum mechanics is the theory to use when it comes to microscopic phenomena: no other theory has been able to describe and pre- dict, for example, atomic behaviour nearly as accurately as quantum me- chanics has been able to. A physicist would also know that microscopic phe- nomena are extremely important when it comes to understanding matter at a larger scale. For example, by understanding the atomic structure you can explain why leaves are green, why certain plastics bend when others break, why metals conduct electricity, why it takes so much energy to heat up water in relation to equal amounts of many other substances, and why chemical
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